论文标题
基本代数
Equidecomposition in cardinal algebras
论文作者
论文摘要
令$γ$为一个可数的群体。索里森的经典定理指出，如果$ x $是标准的borel $γ$ - 空间和$μ$和$ν$，则是$ x $的borel概率措施，它们对每个$γ$ -Invariant子集一致，那么$μ$ $ $和$ν$，则是均等的，即borel的$___________。 $ x $这样，$μ= \sum_γμ_γ$和$ν= \sum_γγμ_γ$。我们将此结果概括为基本代数。
Let $Γ$ be a countable group. A classical theorem of Thorisson states that if $X$ is a standard Borel $Γ$-space and $μ$ and $ν$ are Borel probability measures on $X$ which agree on every $Γ$-invariant subset, then $μ$ and $ν$ are equidecomposable, i.e. there are Borel measures $(μ_γ)_{γ\inΓ}$ on $X$ such that $μ= \sum_γμ_γ$ and $ν= \sum_γγμ_γ$. We establish a generalization of this result to cardinal algebras.
